A community for students.
Here's the question you clicked on:
 0 viewing
MeganDarling
 2 years ago
A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?
3 lbs peanuts, 6 lbs almonds, 2 lbs raisins
8 lbs peanuts, 1 lb almonds, 2 lbs raisins
6 lbs peanuts, 3 lbs almonds, 2 lbs raisins
8 lbs peanuts, 2 lbs almonds, 1 lbs raisins
MeganDarling
 2 years ago
A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins

This Question is Closed

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Start off by defining variables

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1That they add up to 11 pounds haha

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0good, so x y and z add to 11, which means x+y+z = 11

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0that's one equation

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1But then we have to factor in how much they cost..

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0We also know that "The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0this total cost is given to be $21 so 1.5x + 3y + 1.5z = 21

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1so like, 1.50x+3.00y+1.50=21..

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1Haha Okey you already said that x.x my bad

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.11.50z* I meant btw haha. I get that indeed.

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0close, you mean to say 1.50x+3.00y+1.50z=21 but you got it

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1And don't forget twice the peanuts!

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0that's your 2nd equation

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0twice the peanuts as what?

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1it says, the recipe calls for twice as many peanuts as almonds O.o

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0good, so the equation for that is?

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1knew it was wrong x.x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Amount of peanuts = 2 times (amount of almonds)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0y = 2 times x or just y = 2x

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1oh pshh I should have thought of that x.x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0you can use them to solve for x, y and z

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0I'll get you started

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1Lol I can't because I'm stupid, But smart people definitely can haha

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0x+y+z = 11 x+2x+z = 11 3x+z = 11  1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0where are you lost?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1oh okay ! I see now, sorry it's really late and I'm super tired :/

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0so you have 3x+z = 11 7.5x + 1.5z = 21 now

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0solve the first equation for z to get this 3x+z = 11 3x+z  3x = 11  3x z = 11  3x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Since z = 11  3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11  3x) = 21 Solve for x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait, i made a variable mistake...i switched x and y one sec

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Let me fix real quick

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1I was thinking that haha x) ..

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1uhh ? your comment disappeared .. :o

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11  3y  1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11  3y) = 21 Solve that last equation for y

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Solve 6y + 1.5(11  3y) = 21 for y

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1Aw man I have to go to bed soon I'm dead tired x.x

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0What do you get when you solve that equation for y

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1ergh I dunno x.x I'm brain dead

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.0Then give it a break, get some sleep and you'll tackle it in the morning

MeganDarling
 2 years ago
Best ResponseYou've already chosen the best response.1Oh no I keep losing connection >.<
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.